Factual error: When they first meet, Rodrigues tells Blackthorne that aboard his ship there is plenty of food and grog. The problem is that grog was not "invented" until 1740, when it was introduced into the British Navy by Admiral Edward Vernon, who was nicknamed "Old Grog" because of his habit of wearing a grogram coat.
Factual error: Throughout the show, flintlock firearms are used. The show is set in 1600, and the flintlock was not invented until about 1630.